Landau's converse to H\" older's inequality
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909155756867584 |
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| author | Nathanson, Melvyn B. |
| author_facet | Nathanson, Melvyn B. |
| contents | By H\" older's inequality, if $\mathbf{x} \in \ell^p$, then $\mathbf{x}\mathbf{y} \in \ell^1$ for all $\mathbf{y} \in \ell^q$. Landau proved the converse result: If $\mathbf{x}\mathbf{y} \in \ell^1$ for all $\mathbf{y} \in \ell^q$, then $\mathbf{x} \in \ell^p$. This paper proves Landau's theorem and considers a related problem for Hilbert's inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Landau's converse to H\" older's inequality Nathanson, Melvyn B. Classical Analysis and ODEs 26D15 By H\" older's inequality, if $\mathbf{x} \in \ell^p$, then $\mathbf{x}\mathbf{y} \in \ell^1$ for all $\mathbf{y} \in \ell^q$. Landau proved the converse result: If $\mathbf{x}\mathbf{y} \in \ell^1$ for all $\mathbf{y} \in \ell^q$, then $\mathbf{x} \in \ell^p$. This paper proves Landau's theorem and considers a related problem for Hilbert's inequality. |
| title | Landau's converse to H\" older's inequality |
| topic | Classical Analysis and ODEs 26D15 |
| url | https://arxiv.org/abs/2404.00843 |